Alessandra Cipriani

Scaling limit of the odometer in divisible sandpiles

In a recent work Levine et al. (Ann Henri Poincaré 17:1677–1711, 2016. https://doi.org/10.1007/s00023-015-0433-x) prove that the odometer function of a divisible sandpile model on a finite graph can be expressed as a shifted discrete bilaplacian Gaussian field. For the discrete torus, they suggest the possibility that the scaling limit of the odometer may be related to the continuum bilaplacian field. In this work we show that in any dimension the rescaled odometer converges to the continuum bilaplacian field on the unit torus.

Exponential decay of covariances for the supercritical membrane model

We consider the membrane model, that is the centered Gaussian field on

Extremes of Some Gaussian Random Interfaces

{\mathbb{Z}^d}

The limit shape of random permutations with polynomially growing cycle weights

Zd whose covariance matrix is given by the inverse of the discrete Bilaplacian. We impose a

Decay of Correlations for Quantum Spin Systems with a Transverse Field: A Dynamic Approach

{\delta}

The scaling limit of the membrane model

δ-pinning condition, giving a reward of strength